to obtain the solution in a series Example. Use Adomian decomposition method to solve the following linear partial differential equations: ux+y=x+y, i. ii. Ux-Uy = 0, u(0,y) = 0, u(x, 0) = 0. iii. xux + y = 3u, u(0,y) =y, u(x,0) = x. u(0,y) = 0, u(x, 0) = x². iv. ux + y + z = u, U₁t + Uxx = 0, = ut uxx + sin(x), V. vi. vii. viii. Uxx = Utt + U₁ - u Utt = Uxx + Uyy - 7u, u(0,y,z)=1+ e + e², u(x,0,2)=1+ e + u(x,y,0)=1+ex +ex. u(x, 0) = -ex, u(x, 0) = 0. u(x, 0)=sin(x), u(x, 0) = sin(x). u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0. u(0,t) = ezt,ux (0,t) = e−2. Example. Solve the following linear Goursat problem Uxy - u = -x, u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.
to obtain the solution in a series Example. Use Adomian decomposition method to solve the following linear partial differential equations: ux+y=x+y, i. ii. Ux-Uy = 0, u(0,y) = 0, u(x, 0) = 0. iii. xux + y = 3u, u(0,y) =y, u(x,0) = x. u(0,y) = 0, u(x, 0) = x². iv. ux + y + z = u, U₁t + Uxx = 0, = ut uxx + sin(x), V. vi. vii. viii. Uxx = Utt + U₁ - u Utt = Uxx + Uyy - 7u, u(0,y,z)=1+ e + e², u(x,0,2)=1+ e + u(x,y,0)=1+ex +ex. u(x, 0) = -ex, u(x, 0) = 0. u(x, 0)=sin(x), u(x, 0) = sin(x). u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0. u(0,t) = ezt,ux (0,t) = e−2. Example. Solve the following linear Goursat problem Uxy - u = -x, u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:to obtain the solution in a series
Example. Use Adomian decomposition method to solve the following linear
partial differential equations:
ux+y=x+y,
i.
ii.
Ux-Uy = 0,
u(0,y) = 0, u(x, 0) = 0.
iii.
xux + y = 3u,
u(0,y) =y, u(x,0) = x.
u(0,y) = 0, u(x, 0) = x².
iv.
ux + y + z = u,
U₁t + Uxx = 0,
=
ut uxx + sin(x),
V.
vi.
vii.
viii.
Uxx = Utt + U₁ - u
Utt = Uxx + Uyy - 7u,
u(0,y,z)=1+ e + e², u(x,0,2)=1+ e +
u(x,y,0)=1+ex +ex.
u(x, 0) = -ex, u(x, 0) = 0.
u(x, 0)=sin(x), u(x, 0) = sin(x).
u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0.
u(0,t) = ezt,ux (0,t) = e−2.
Example. Solve the following linear Goursat problem
Uxy - u = -x,
u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
